What will happen if Labour implodes politically, either in the days or weeks ahead or at the coming general election? Stoke-on-Trent is worth looking at in this context because the party that once dominated Potteries politics underwent its own gentle implosion a few years ago.

The result? A cross-party coalition trying to hold local government together, supported by Labour, the Lib Dems and the Tories – and opposed by nine councillors from the British National party. The BNP is looking to alienated Stoke voters to boost its share of tomorrow's poll in the West Midlands and – perhaps – elect a BNP candidate for Europe.

With its famous pottery museums, heritage trails and designated "Cultural Quarter", Stoke looks at first glance as if it has adapted to post-industrial life as well as other British cities. But appearances on a bright spring morning, when I visited, can be deceptive.

Over the past 40 years the six-town conurbation known as the Potteries has suffered a string of misfortunes, economic and political. It lost its steel mills, coal mines – "pits and pots" – and the bulk of its pottery production. The North Staffs regeneration plan has been late in coming, and many lost jobs have been replaced with £6-an-hour call centre and warehousing work.

The city's three MPs are still Labour, as they have been since 1945, but none has been an imposing national figure for decades. Cynthia Mosley (Sir Oswald's wife) was once an MP here. At local level Labour hegemony has fragmented to the point where the BNP boasts nine city councillors (to Labour's 16) and hopes Stoke voters will help elect Nick Griffin's lieutenant and national spokesman, Simon Darby, as a West Midlands regional MEP in tomorrow's European elections.

Bolder BNP strategists even claim they could get their first Westminster MP here in 2010 if unemployment – overall "worklessness" is above average in Stoke – stays above three million. Labour takes the BNP threat seriously, but not that seriously: BNP candidates saved their local deposits in 2005 but got a maximum 15% in all three seats, behind the main parties.

The Tory chairman, Eric Pickles, thinks the BNP may pick up one or two European seats – or may flop. As the Financial Times reported yesterday, Pickles blames Labour for neglecting core voters and giving the BNP the chance to win them over. The Dagenham MP, Jon Cruddas, who fights the BNP in its London stronghold, says much the same: it is the price of the Blair-Brown centrist strategy.

Privately, some of Gordon Brown's lieutenants fear there could be four or five BNP MEPs, each with access to £250,000 worth of funds, when the results are announced across Europe late on Sunday. "It would change the face of British politics," warns one minister, who cites the French National Front's rise on the back of European votes. The far right hopes to do well across the recession-hit EU.

"Stoke has a very resentful population; it's very upset with Labour," explains Darby. He describes how Steve Batkin, one of three BNP councillors in Bentilee ward on the Alton Towers side of the city, "walks around all day with his garden tools doing old people's gardens. They like him. We are replacing people who treated the population with absolute contempt."

From Kent to Cumbria this is the new "community politics" face of the BNP, one whose hostility to immigrants, asylum seekers and Europe is just below the surface but not on display. Would-be BNP voters tend to be white, working-class men who live in rented accommodation, have low educational achievement and read anti-immigrant tabloids, Ipsos-Mori pollsters told the FT. No surprise there, for the alienation of "white van man" from modern Britain has been well documented.

The BNP's ambitions for Stoke are not immediately apparent on the ground either. Voters I spoke to in Hanley's Potteries shopping centre – close to the statue of Stanley Matthews, the Hanley-born legend of English football – did not mention the BNP unless prompted.

"They frighten me. I don't like it," said an old lady, wrinkling her nose.

"I don't get any trouble," said a rare black voter (Stoke's black and minority population is around 5%; Polish coal miners have long been there, too).

Just one passerby, a retired lecturer and Tory, admitted: "I'm thinking of voting BNP because the main parties never listen."

Anger against the council is strong and includes favourite BNP themes such as preference allegedly given to immigrants in the housing queue and the "sweetheart" land deal (officials deny it) that is allowing Muslims in Shelton to build their own mosque.

In Abbey Green ward, on the edge of 250,000-strong Stoke, the story is the same. "I think the BNP nearly got elected here last time," said a man walking with his children in what is an overwhelmingly white estate of neat, red-brick, interwar housing, a mixture of private and council.

He's wrong. Here and elsewhere BNP candidates took all three seats, including Alby and Ellie Walker, who Labour critics privately admit would be "pleasant and cheery people if you met them in the pub". Some say the couple's attitudes on race and multicultural are little different from Labour's of yesteryear.

There are two basic answers to the BNP challenge, says Geoff Bagnall, who runs the Unity ceramics-based trade union whose membership has fallen from 31,000 to 5,000 during years of economic decline.

"The Labour party must go back to its roots and represent people properly," he said. "And there must be long-term government regeneration, bringing new jobs and better education to the city."

Easier said than done. Mike Wolfe, the energetic ex-Labour man who led the campaign for a directly elected mayor in Stoke in 2002 and won the post himself, says Stoke has great potential and fantastic road, rail and [nearby] air communications; it's "virtually a roundabout" at the heart of Britain. Other cities reinvented themselves. Why not Stoke?

But Wolfe proved too much of a loner, and Labour's 60-seat monopoly of the council was fast collapsing into seven or eight rival groups. His Labour successor since 2005, Mark Meredith ("the least unpopular candidate for the nomination"), has alienated much of his base, not least by bringing controversial private contractor Serco in to manage a disruptive reorganisation of local schools.

To add to the woes in Stoke, Meredith and the Tory group leader, Roger Ibbs, have both been arrested this year on suspicion of corrupt dealings, and police investigations continue. Officials, eager to promote overdue regeneration plans, are largely running the town hall, where paid councillors in all three main parties are now part of the mayor's coalition.

As for the BNP, it is fielding candidates for the first time across the municipal boundary in the two most deprived wards of adjacent Newcastle-under-Lyme. The campaign is buttressed by "Punish the pigs" leaflets – a gesture to the expenses row that has tainted Labour in Stoke, as elsewhere.

So Stoke is the place where Old Labour faltered, but many New Labour ideas have collided with harsh realities on the ground. Alarmed by the BNP, ministers in London are finally taking it seriously. The wife of the local government minister, John Healey, hails from Stoke. The message that Stoke's introverted political culture – its talent is too often lured to Birmingham or Manchester – needs more help from outside has finally got through. Many things are getting better, but slower and later than elsewhere.

Last October, punch-drunk Stoke residents in the six Potteries towns (Arnold Bennett's "five towns" novels deliberately ignored Fenton) voted to reverse the elected mayor experiment in favour of a cabinet-style council. Speculation persists that Whitehall may take over to fill the vacuum until fresh elections. The BNP has stepped in to fill a Labour vacuum that Lib Dems (just five councillors here) have filled elsewhere.

It amounts to a major political train crash, but Mike Wolfe says Stoke is just a more dramatic version of what is going on in other troubled northern cities. The famous name of Wedgwood has been bought from administration by a US firm. "The BNP is a symptom, not a cause" of Stoke's problems, admits the local MP Mark Fisher.

Simon Darby knows all the regional percentages needed under the European elections' regional voting system to elect a BNP MEP here and elsewhere. Nick Griffin, a regular visitor to Stoke, has the best chance in the nearby North West region (8.5% – just 2% more than last time) compared with an 11% hurdle in the West Midlands.

Turnout among supporters of the mainstream parties is therefore crucial tomorrow to minimise the impact of the BNP's still-modest base (they have barely 100 party members in Stoke, according to last year's leaked party list). But as the PM's colleagues whisper, it does no good just to condemn the BNP, as Gordon Brown sometimes thinks (yesterday's Guardian letter, for example).

"Be sure to vote on June 4 if you don't want the BNP," has become a campaign slogan endorsed by all the main parties. But what if many angry voters decide they do?